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61804 - Numerical Analysis (2015/2016) Stampa

Course syllabus

  • Error analysis
    • Radix-2 representation.
    • Floating-point numbers and machine precision.
    • Inerent error. Estimate for rational functions.
    • Algorithmic error.
    • Total error.
  • Solving nonsingular linear systems
    • Numerical solution of linear systems (direct method of Gaussian elimination).
    • Conditioning of matrices.
    • Complexity and algorithmic error of Gaussian elimination.
  • Basic concepts of linear algebra: geometric interpretation of vectors and matrices
    • Scalar product and orthonormal bases.
    • Matrices and geometric linear transformations .
    • Null space, range and rank.
    • Orthogonal matrices: rotations, reflections, QR factorization.
  • Least-squares approximate solution of linear systems
    • Geometric framework of the problem.
    • Normal equations.
    • Least-squares solution by orthogonalization.
  • Spline interpolation
    • Definition of interpolating splines.
    • Computational procedure.
    • Mathematical and numerical properties.
  • Basic concepts of linear algebra: eigenvalues
    • Eigenvalues, eigenvectors, eigenspaces.
    • Characteristic polynomial.
    • Similarity relations and diagonalization.
    • Applications.
  • SVD and applications to least squares
    • Singular value decomposition (SVD) and relationships with eigenvalues
    • Geometric properties of SVD and relationships with rank.
    • Generalized inverse and conditioning.
    • Solution of the least-squares problem by SVD.
    • Application to discrete data approximation (Smoothing).
  • Numerical treatment of eigenvalues
    • Numerical properties: conditioning and localization.
    • The iterative power method and variants.
    • Other numerical methods: similarity reduction to simplified form, the QR method.

PC exercises in C and Matlab language are planned.

Language

Italian

Teacher

Fabio Di Benedetto

Teaching style

In presence

Lesson timetable

Monday: 14:00 - 16:00, room 505
Thursday: 14:00 - 16:00, room 505

Attendance

Not required

Course hour allocation

This course consists of 48 hours of lectures.

Statistics

Average Marking Number of Exams Year
23.538262013
25.000222012
25.000102011